6. Let X be a random variable taking values in the non-negative integers \{0, 1, 2, 3, ...\}. Show that $E(X) = \sum_{i=0}^{\infty} P(X > i)$. Hint: Use the fact that $\sum_{i=0}^{\infty} P(X > i) = \sum_{i=0}^{\infty} \sum_{k=i+1}^{\infty} P(X = k)$, and then change the order of summation.
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